I would like to use the function " ConjugacyClassesMaximalSubgroups " in
Gap, for groups PSL(5,2), PSL(6,2), PSL(7,2). But it seems that there is a
problem for running time or something else. I will be more grateful for any
help or comments.

As Dima Pasechnik has already said, these are rather large groups on which to
perform this sort of computation directly using general purpose machinery.

On the other hand, maximal subgroups of classical groups (including PSL) are
described by a theorem of Aschbacher, see: